1. Gauss's Theorem and Application to an Infinitely Long Charged Wire Gauss's Theorem: The total electric flux through a closed surface is equal to 1 ε 0 \frac{1}{\varepsilon_0} ε 0 1 times the total charge enclosed. ∮ E ⋅ d A = Q enc ε 0 \oint \mathbf{E} \cdot d\mathbf{A} = \frac{Q_{\text{enc}}}{\varepsilon_0} ∮ E ⋅ d A = ε 0 Q enc Application to an Infinitely Long Charged Wire For a wire with charge density λ \lambda λ (charge per unit length) at a distance r r r , using a cylindrical Gaussian surface: E ⋅ ( 2 π r L ) = λ L ε 0 E \cdot (2\pi r L) = \frac{\lambda L}{\varepsilon_0} E ⋅ ( 2 π r L ) = ε 0 λ L Solving for E E E : E = λ 2 π ε 0 r E = \frac{\lambda}{2\pi \varepsilon_0 r} E = 2 π e 0 r λ 📌 The field is radially outward if λ > 0 \lambda > 0 λ > 0 and inward if λ < 0 \lambda < 0 λ < 0 . 2. Potential Energy of a System of Two Point Charges The electrostatic potential energy of two point charges q 1 q_1 q 1 and q 2 q_2 q 2...
jeet pardhi
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